Can a monitor receive and transmit simultaneously via HDMI?

I have the following problem:

I plan to upgrade my multimedia station inexpensively.

I'll get a 4K monitor with 2 HDMI 2.0 ports, a soundbar with an HDMI port and a PS5.

The following question: Can I connect the soundbar and PS5 to the monitor at the same time? I don't want to switch the soundbar between the PS5 and the monitor, because I don't know whether this will increase the input delay.

So I would send the sound and audio from the PS5 to the monitor, this shows the image and sends the sound to the soundbar.

Is that possible?

If anyone has any questions about the products:

https://www.amazon.de/...B07BBRLTRH

https://teufel.de/cinebar-11-21-set-105373000#pdp-specifications

Only input> output possible.

No bridge or anything

So would I have to use the soundbar as a bridge? Or is there a more common method

The monitor only has 2x HDMI in and can (is not a TV) logically no ARC. So you won't be able to avoid putting the soundbar in between.